Steady State Analyses for Reactive Distillation Control:

An MTBE Case Study

Bhanu Pratap Singh, Ram Singh, M V Pavan Kumar and Nitin Kaistha[*]

Department of Chemical Engineering

Indian Institute of Technology

Kanpur 208016 (INDIA)

Abstract

Systematic steady analyses are conducted to synthesize effective control structures for an MTBE reactive distillation column. The control objective is to maintain the product purity and reaction conversion for changes in the production rate and feed composition. The steady state relations between manipulated variables (inputs), namely, fresh feed flows and reboiler duty, and potential controlled variables (outputs), namely, tray temperatures and compositions, are studied to assess the steady state multiplicity and linearity of the input-output relations. Input-output pairings that are sensitive, away from the zone of steady state multiplicities and nearly linear about the base case operating condition, are preferred. A control structure that controls a sensitive tray temperature in the stripping section using the reboiler duty and maintains the isobutene composition on a reactive tray using one of the fresh feeds is found suitable. Controlling a reactive tray composition is essential for balancing the fresh feeds into the column as per the reaction stoichiometry. The tray locations for temperature and composition measurements must be chosen so that dynamic instability due to interaction between the two control loops is avoided.

Keywords: Reactive distillation, control structure, process intensification

Introduction

The operation and control of reactive distillation (RD) columns is a complicated issue that must be addressed at the design stage for successful implementation of the technology. The coupling of reaction and separation in a single unit makes the system highly non-linear so that predicting column behavior in the presence of disturbances and changed operating conditions is non-trivial. The control degrees of freedom vis-à-vis conventional processes is reduced so that the separation and reaction extent must be regulated using fewer available valves. The operability and control issue is further compounded by the existence of multiple steady states that are routine phenomena in RD systems (Jacobs and Krishna (1993); Nijhuis et al (1993); Ciric and Miao (1994); Sneesby et al (1998); and Chen et al (2002)). Formulating the best operating strategy can be quite complex and non-intuitive. A robust control strategy that ensures safe, stable and economic operation in the presence of disturbances is thus essential.

In recent years, many articles have appeared in the literature on the control of RD columns. Prominent among these is the pioneering work of Al-Arfaj and Luyben who have published a series of articles on RD control (Al-Arfaj and Luyben (2000); Al-Arfaj and Luyben (2002a-d); and Al-Arfaj and Luyben (2004)). Their work offers much insight on key issues that a RD column control system must address. Control of an RD column with ideal VLE is studied in Al-Arfaj and Luyben (2000). The authors show that controlling a tray temperature in the stripping section and a composition in the reactive section provides good control. The control of the industrially important methyl acetate column is studied in Al-Arfaj and Luyben (2002a). A control structure that maintains a tray temperature in both the reactive and stripping sections using the fresh acetic acid and methanol feeds respectively, provides the best control of all the control structures studied. The column is operated at fixed reflux ratio and the reboiler duty is the production rate handle. It is worth mentioning that this is the control structure implemented at Eastman. Al-Arfaj and Luyben have also studied the control of an olefin metathesis column (Al-Arfaj and Luyben (2002b)), an ethylene glycol column (Al Arfaj and Luyben (2002c)), an ETBE column (Al-Arfaj and Luyben (2002d)) and the design and control of a RD based process for TAME production (Al-Arfaj and Luyben (2004)).

Other authors have also studied the control of RD columns. These include the work of Vora and Daoutidis (1999) who study the non-linear control of an ethyl-acetate column. Sneesby et al (1999) study the two point control of an ethylene glycol column. Grüner et al (2002) apply asymptotically exact input-output linearization to derive and implement a control law on a simulated industrial RD column operated by Bayer AG. Pattern based control of an ETBE column is studied by Tian et al (2003). Most of the work is however esoteric and un-necessarily mathematical and does not provide much intuitive insight on RD control. The rationale behind why a particular control structure gives better performance than others does not come across clearly. This work is motivated by this need to better understand why a control structure is preferred over others through a systematic analysis of the governing steady state input-output relationships for the different control structures.

RD Control

An RD column must be operated so that the product purity and reaction conversion are maintained close to their design values for major disturbances entering the column. A robust control system needs to put in place that can regulate the column for anticipated production rate changes and changes in the feedstock composition, the principal disturbances into a column. In the design of such a control system, the selection of the control structure is the most crucial decision.

A control structure refers to the number of control loops and the specific input-output pairing used in the loops. Potential input variables are the reflux rate, reflux ratio, reboiler duty, reboil ratio, distillate rate, bottoms rate and the fresh feeds. Potential output variables are easily measurable variables such as tray / stream temperatures and compositions. There are thus several possible input (manipulated) variables and output (controlled) variables even in a simple RD column. The various permutations and combinations lead to a large number of possible control structures from which a small set of “good” control structures must be chosen. Evidently, the key to successful column operation is this screening of control structures to zero in on the most appropriate controlled variables and effective handles to manipulate them so that by maintaining the controlled variables at their set-points, the purity and conversion of the column remain near the design specifications. Indeed, for a good control structure, other control system design decisions such as the choice between sophisticated versus simple control algorithms becomes obvious in that simple PI control should suffice. On the other hand, no amount of sophistication in the control algorithm can compensate for an inherently poor control structure.

A good control structure is one that rejects disturbances effectively. In order to do so, controlled variables that are sensitive to the occurrence of the primary disturbances should be chosen so that timely control action can be initiated (Moore (1992)). Also, the manipulated variables used for control should affect the controlled variables in a substantial and easily predictable way. Such a choice assures enough “stick” for column regulation even for large disturbances. At steady state, linear or nearly linear input-output relationships are certainly desirable so that the process gain does not change appreciably. In case multiple control loops are used, the input output pairings should not cause stability problems due to interaction between the loops. Last but not least, since sensor measurements are never exact, the column performance should be robust to typical measurement errors or errors in the set-point inputs.

Systematic steady state analyses can be conducted to reveal the control structure/s that provides effective column regulation for the primary disturbances into a column. These analyses include sensitivity studies for obtaining potential controlled variables that are sensitive to disturbances and manipulated variables. For different control structures, the column response in terms of performance variables such as steady state product purity and conversion, and the steady state input-output relationship that a controller sees, can be studied for the major anticipated disturbances. From these analyses, good control structures are obtained as the ones that ensure product purity and conversion within acceptable limits while avoiding steady state multiplicities with nearly linear input-output relations.

This simple philosophy for control structure synthesis is demonstrated on a double feed MTBE RD system in this work. The approach taken is to study the effect of varying the input handles about their base case values, on the column outputs to identify potential input-output pairings. Pairings that are sensitive, avoid multiplicities and give nearly linear input output relationships are short listed. Next, control loops are systematically added and the column steady state response to the primary disturbances evaluated until we arrive at the simplest control structure(s) that satisfies the control objective of maintaining conversion and purity.

For the double feed MTBE case study reported here, the preferred control structure operates at fixed reflux ratio and maintains a stripping section tray temperature by manipulating the reboiler duty. A reactive tray composition is controlled by manipulating one of the fresh feed rates in order to balance the fresh feed as per the reaction stoichiometry. Both the fresh feeds can be used as the manipulation handle in the composition loop. The tray location for the composition measurement must be carefully chosen to avoid stability problems due to interaction with the temperature loop.

Steady State Multiplicities

We distinguish between two types of multiplicities: output multiplicity and input multiplicity. The former refers to multiple output values for the same input specification while the latter refers to multiple input specifications giving the same output. This is illustrated in Figure 1 . From a control perspective, input variables are manipulated variables such as the reboiler duty or reflux ratio while output variables are potential controlled variables such as tray temperatures / compositions. Wang et al (2003) study the effect of multiplicities on the design of a control system for an MTBE column.

The choice of the control structure substantially affects the number of steady state multiplicities and the size of the operating space in which these multiplicities occur. In other words, the complexity of the input-output relationships depends on the control structure used. The control structure chosen must avoid output multiplicities to ensure that the column does not drift from say a high conversion steady state to a low conversion steady state even though there is no apparent change in the inputs to the column.

The consequences of input multiplicity are not as severe. If possible, it should be avoided as the sign of the gain between the input and output variable changes depending on the column operating condition. Also, if the output variable is used in a control loop, the range of feasible set-point specifications becomes limited so that measurement biases can drive the control system to seek an infeasible steady state.

The MTBE Reactive Distillation Column

The primary reaction in MTBE production is the etherification of isobutene with methanol to form MTBE in the presence of a strong acid catalyst. The MTBE RD column studied is shown in Figure 2. The base case operating conditions and design parameters are given in the Figure. For VLE calculations, the liquid phase activity coefficients are modeled using the Wilson equation. The Wilson parameters are tabulated in Table 1. The vapor phase is assumed ideal. An activity based rate expression is used to model the reaction kinetics as

The reaction rate constant and equilibrium constant are modeled as

and

The column operates at a high reflux ratio of 7 with a base case conversion of 91.95% with 99.86% pure MTBE leaving from the bottoms. A control system that maintains the product purity and reaction conversion near the design values is desired. It should provide smooth transitions for production rate changes and compensate for any changes in the butene feed composition. In order to synthesize such a control structure the effect of the various potential manipulated variables on the column tray temperatures and compositions is studied.

Effect of Column Inputs on Output Variables

The potential input variables or valves that can be manipulated to regulate the column are the two fresh feeds, the reflux rate and the reboiler duty. It is also possible to maintain the flow ratios of two streams such as the reflux ratio or the reboil ratio. Manipulating the reflux rate or ratio for column regulation is not a good idea since the hold up (or catalyst weight) on each reactive stage in an RD column is large so that the column response can be extremely sluggish. In contrast, manipulating the reboiler heat duty causes an immediate change in the vapor rate throughout the column. These dynamic considerations indicate that fixed reflux rate or reflux ratio operating policies are preferable and the reboiler duty and feed flows can be used for regulating the separation and the reaction in the column.

Now in order to decide between the fixed reflux rate vs fixed reflux ratio policy, Figure 3 plots the steady state purity and conversion as the reboiler duty is varied with the feed conditions at their base case values for the two operating policies. Output multiplicity is evident for both the fixed reflux rate and the fixed reflux ratio policies. It is however noted that in the latter case, the base case point is away from the zone of output multiplicity while output multiplicity occurs in the former even for the base case. The column can thus drift from a high conversion steady state to a low conversion steady state even as the reboiler duty and the feed conditions remain the same for a fixed reflux rate. The same cannot happen in case the reflux ratio is kept fixed. Also the range of reboiler duty about the base case for which the conversion and purity are acceptable is greater if the fixed reflux ratio policy is used. Therefore, the fixed reflux ratio policy is preferred.

Having decided on maintaining a fixed reflux ratio, the response of the tray temperatures to changes in one of the remaining input variables is studied. Figure 4 plots the steady state tray temperature response to changes in the reboiler duty about the base case respectively. All the tray temperatures, especially for trays 11 to 14 in the stripping section are quite sensitive to changes in the reboiler duty. A small zone with output multiplicities is observed. This zone is however away from the base case so that reboiler duty may be used to maintain a sensitive tray temperature in the stripping section, as in ordinary distillation.

Next, the effect of varying the fresh feed flows on the column tray temperatures is studied. The tray temperatures for changes in fresh methanol are shown in Figure 5. Substantial input multiplicity in the temperature of reactive trays is evident from the plots. The multiplicity is also seen if the fresh butene feed flow is varied (figure not shown). The process gain thus changes sign depending on the operating condition. Also it is seen that the base case tray temperatures differ from the maximum tray temperatures by only about 2 oC so that sensor bias can cause an infeasible temperature specification. The reactive tray temperature should therefore not be controlled.

An alternative to reactive tray temperature measurement is the tray composition. Figure 6 illustrates the isobutene composition response to changes in the fresh butene feed and the fresh methanol feed for the reactive trays. Reactive trays that are sensitive and do not show input / output multiplicity are seen in the plots eg tray 3 composition for both the fresh feeds. These measurements can be used for balancing the fresh feeds into the column to be nearly stoichiometric, as shown in the next section.

Control Structure Synthesis

We start with the simplest column operation strategy of no control and then keep adding complexity in the form of control loops until we arrive at the simplest control structure that achieves the desired control objective. The objective here is to maintain the product purity and reaction conversion for the principal disturbances, namely change in production rate and feeds composition. Operating the column at fixed reflux ratio and a fixed reboiler duty is the starting point. The fresh feeds are assumed under flow control. Even for a relatively small change of +10% in the fresh methanol feed rate, the MTBE product purity drops dramatically to less 95%. The fresh feed rates may be varied by an operator or may be off due to the typically high errors involved in flow measurements. This is because one of the reactants (methanol) becomes excess and exits with the product stream, reducing its purity.